The current through a wire varies with time as `I= I_(0) + alpha t `, where `I_(0) ` = 1 A and `alpha =4 As^(-1)` . The charge that flows across a cross-section or the wire In first 10 seconds is ....

Options

A. 210 C
B. 300 C
C. 150 C
D. 250 C

Answer

B

Explanation

300 C
Current , I `(dq)/(dt) = I_(0) + alpha` t
`therefore dq = (I_(0) + alpha t ) ` dt
Integrating on both sides,
Q = `int dq = int_(t = 0 )^(t = 10 ) ( I_(0) + alpha t ) ` dt
= `int_(0)^(10) I_(0) dt + int_(0)^(10) alpha t dt `
`= I_(0) int_(0)^(10) dt + alpha int_(0)^(10)t dt `
=` I_(0) [t]_(0)^(10) + alpha [(t^(2))/(2) ]_(0)^(10)`
`= 10 I_(0) + 50 alpha `
Substituting `I_(0) = 10 and alpha = 4 `
Q = 10 (10) + 50 (4) 300 C